The traditional term among writers is often “murder your darlings.” This phrase is not always understood and does repel by its overly dramatic word choice. These days we delete files, unlike the old days when the technical term and the code command was to “kill” a file.
What you are looking for, in order to change or delete, are words, phrases, scenes, characters, or subplots that are too brilliant, too clever, too glow-in-the-dark, so that they don’t fit into the prose or story organically. They stick out like that cupboard door left open at eye height. In revision, you need to close the door.
These are often hard to see for yourself, especially after several revisions. You become work-blind to them. You can best find them by watching your own reactions.
Yes, you are supposed to write in an interesting style, but not in one that jerks the reader out of the story to yell in their face, “See how cleverly I write?” (The Time Traveler’s Wife is a classic example of this flaw.) Yes, you are supposed to have characters who aren’t cardboard or pabulum, but that doesn’t mean making everyone weird for weird’s sake. Yes, this is an area with a wide fuzzy border, where stay or delete, good or go, is hard to call. Much depends on your intended readership, your genre, the reaction you’re going for. If you’re writing humor, what is normally a flaw gets you laughs for incongruity.
So let’s assume you’re not writing humor, litfi, or anything else that inverts the rules.
In this case, look out for anything that seems so important, so clever, so endearing, but that, when closely examined, really isn’t necessary.
Look at The Lord of the Rings. (Yes, this is a great work, but it’s a long ways from a perfect work.) Consider the subplot of the ents. This is an example of something completely necessary. Without it, there would have to be something new invented to bring down Saruman. Bringing in the ents is one reason to pull the original Walkers into three parties.
Look at Tom Bombadill. This is a classic example of a pet that should be deleted. This character has swelled up until it is very demanding of attention, with all his songs (annoying as they are), which really has no purpose.
Oh, he rescues the hobbits from the evil willow. No, the evil willow exists to introduce Tom Bombadill.
Notice how seamlessly Peter Jackson removed the whole episode, to the happy relief of everyone down the decades who had read that segment once then always skipped it.
Obviously, JRRT thought Tom was one of his cleverest creations and every reader would love him. I understand George Lucas was very fond of Jar-jar Binks, too.
Tom B. was one of those intrusions from writing to amuse children that JRRT should have excised.
Also among extraneous characters, let us, before we go, consider Glorfindel.
“Who?” asks everyone who only saw the movies.
Jackson used Arwen to rescue Frodo, thereby giving her more existence than a mentioned mead of honor. Those of us who read it often kept waiting for Glorfindel to show up again, but he doesn’t, after all his build-up. In this case, JRRT should have done some character merging. He could just as well have made the heroic elven rescuer Elrond or Legolas, rather than bring in an icky girl — or create another single-use disposable character.
Consider this when looking over your list of characters.
If you just can’t stand life without that one, consider it a signal that this is a pet, a darling, and it probably needs its own project to star in.
In watching your reactions to your own work, “Squee! I love this!” is a warning. So is a great big smile of delight over a phrase (it’s just a phrase) or a character or a speech. The parts of a larger story should feel right, proper, correct, and satisfying, but they shouldn’t be show-stoppers you applaud. If it makes you think how clever the character is — maybe, maybe not. If it makes you think how clever the writer is — out with it!